Large deviation approach to non equilibrium processes in stochastic lattice gases

Bulletin of the Brazilian Mathematical Society

Volumn 37, Issue 4, 2006, Pages 611-643

  Bertini, Lorenzo ^a   De Sole, Alberto ^b   Gabrielli, Davide ^c   Jona Lasinio, Giovanni ^d   Landim, Claudio ^e,f  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b HARVARD UNIVERSITY   (United States)

^c UNIVERSITY OF L'AQUILA   (Italy)

^d UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^e IMPA   (Brazil)

^f UNIVERSITÉ DE ROUEN   (France)

Author keywords

Hydrodynamic limit; Interacting particle system; Large deviation

Indexed keywords

EID: 33845737837     PISSN: 16787544     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00574-006-0031-0     Document Type: Article

References (26)

1. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Fluctuations in stationary non equilibrium states of irreversible processes. Phys. Rev. Lett., 87 (2001), 040601.
2. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Macroscopic fluctuation theory for stationary non equilibrium state. J. Statist. Phys., 107 (2002), 635-675.
3. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Large deviations for the boundary driven simple exclusion process. Math. Phys. Anal. Geom., 6 (2003), 231-267.
4. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Current fluctuations in stochastic lattice gases. Phys. Rev. Lett., 94 (2005), 030601.
5. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Non equilibrium current fluctuations in stochastic lattice gases. Preprint 2005, arXiv: condmat/0506664.
6. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Large deviations of the empirical current in interacting particle systems. Preprint 2005, arXiv: math.PR/0512394.
7. L. Bertini, D. Gabrielli and J.L. Lebowitz, Large deviations for a stochastic model of heat flow. J. Statist. Phys., 121 (2005), 843-885.
8. T. Bodineau and B. Derrida, Current fluctuations in non-equilibrium diffusive systems: an additivity principle. Phys. Rev. Lett., 92 (2004), 180601.
9. T. Bodineau and B. Derrida, Distribution of current in non-equilibrium diffusive systems and phase transitions. Preprint 2005, arXiv: cond-mat/0506540.
10. T. Bodineau and G. Giacomin, From dynamic to static large deviations in boundary driven exclusion particles systems. Stoch. Proc. Appl., 110 (2004), 67-81.
11. A. De Masi, P. Ferrari, N. laniro and E. Presutti, Small deviations from local equilibrium for a process which exhibits hydrodynamical behavior. II. J. Statist. Phys., 29(1982), 81-93.
12. B. Derrida, J.L. Lebowitz and E.R. Speer, Free energy functional for nonequilibrium systems: an exactly solvable model. Phys. Rev. Lett., 87 (2001), 150601.
13. B. Derrida, J.L. Lebowitz and E.R. Speer, Large deviation of the density profile in the steady state of the open symmetric simple exclusion process. J. Statist. Phys., 107 (2002), 599-634.
14. M.D. Donsker and S.R.S. Varadhan, Large deviations from hydrodynamic scaling limit. Comm. Pure Appl. Math., 42 (1989), 243-270.
15. C. Enaud and B. Derrida, Large deviation functional of the weakly asymmetric exclusion process. J. Statist. Phys., 114 (2004), 537-562.
16. G. Eyink, J.L. Lebowitz and H. Spohn, Hydrodynamics of stationary nonequilibrium states for some lattice gas models. Commun. Math. Phys., 132 (1990), 253-283.
17. G. Eyink, J.L. Lebowitz and H. Spohn, Lattice gas models in contact with stochastic reservoirs: local equilibrium and relaxation to the steady state. Commun. Math. Phys., 140 (1991), 119-131.
18. M.I. Freidlin and A.D. Wentzell, Random perturbations of dynamical systems. Springer-Verlag, Berlin, New York 1998.
19. A. Galves, C. Kipnis, H. Spohn, Unpublished manuscript (1983).
20. R. Graham and T. Tel, Nonequilibrium potential for coexisting attractors. Phys. Rev., A 33 (1986), 1322-1337.
21. C. Kipnis and L. Landim, Scaling limits of interacting particle systems, Springer-Verlag, Berlin, New York, (1999).
22. C. Kipnis, C. Marchioro and E. Presutti, Heat flow in an exactly solvable model. J. Statist. Phys., 27 (1982), 65-74.
23. C. Kipnis, S. Olla and S.R.S. Varadhan, Hydrodynamics and large deviations for simple exclusion processes. Commun. Pure Appl. Math., 42 (1989), 115-137.
24. L. Onsager and S. Machlup, Fluctuations and irreversible processes. I Phys. Rev., 91 (1953), 1505-1512;
25. Fluctuations and irreversible processes. II Phys. Rev., 91 (1953), 1512-1515.
26. H. Spohn, Long range correlations for stochastic lattice gases in a nonequilibrium steady state. J. Phys., A 16 (1983), 4275-4291.